An efficient nonnegative matrix factorization approach in flexible kernel space
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
A doubly weighted approach for appearance-based subspace learning methods
IEEE Transactions on Information Forensics and Security
Nonlinear non-negative component analysis algorithms
IEEE Transactions on Image Processing
Sequential coordinate-wise DNMF for face recognition
ICAISC'10 Proceedings of the 10th international conference on Artificial intelligence and soft computing: Part I
Clustering in extreme learning machine feature space
Neurocomputing
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Plenty of methods have been proposed in order to discover latent variables (features) in data sets. Such approaches include the principal component analysis (PCA), independent component analysis (ICA), factor analysis (FA), etc., to mention only a few. A recently investigated approach to decompose a data set with a given dimensionality into a lower dimensional space is the so-called nonnegative matrix factorization (NMF). Its only requirement is that both decomposition factors are nonnegative. To approximate the original data, the minimization of the NMF objective function is performed in the Euclidean space, where the difference between the original data and the factors can be minimized by employing L 2-norm. In this paper, we propose a generalization of the NMF algorithm by translating the objective function into a Hilbert space (also called feature space) under nonnegativity constraints. With the help of kernel functions, we developed an approach that allows high-order dependencies between the basis images while keeping the nonnegativity constraints on both basis images and coefficients. Two practical applications, namely, facial expression and face recognition, show the potential of the proposed approach.